An executive has two routes that she can take to and from work each day. The first is by interstate; the second requires driving through town. On the average it takes her 33 minutes to get to work by the interstate and 35 minutes by going through town. The standard deviations for the two routes are 6 and 5 minutes, respectively. Assume the distributions of the times for the two routes are approximately normally distributed.
(a) What is the probability that on a given day, driving through town would be the quicker of her choices?
(b) What is the probability that driving through town for an entire week (ten trips) would yield a lower average time than taking the interstate for the entire week?